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O PTIMAL M ONETARY P OLICY FOR THE
M ASSES
James Bullard (Federal Reserve Bank of St. Louis)
Riccardo DiCecio (Federal Reserve Bank of St. Louis)
Adam Smith Panmure House Lecture
Edinburgh, United Kingdom
Oct. 24, 2018
Any opinions expressed here are our own and do not necessarily reflect those of the FOMC.
I NTRODUCTION
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Introduction
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I NTRODUCTION
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A DAM S MITH AND
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INEQUALITY
The thrust of Adam Smith is to argue that when all households pursue their own
self-interest, society as a whole attains the best available allocation of resources.
Yet Adam Smith also stated that “Wherever there is great property there is great
inequality.”
Are these views contradictory?
The literature on heterogeneity and monetary policy helps to frame answers to this
question.
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I NEQUALITY AND MONETARY POLICY
Can monetary policy be conducted in a way that benefits all households even in a
world of substantial heterogeneity?
The answer in this paper is “yes.”
C ONCLUSIONS
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S OME RECENT LITERATURE
Kaplan, Moll and Violante (AER, 2018):
NK model with heterogeneous households (“HANK”); reasonable Gini coefficients.
The monetary policy transmission mechanism is substantially altered relative to standard
model.
Bhandari, Evans, Golosov and Sargent (Working paper, NYU, 2018):
Incomplete markets, nominal friction, heterogeneous households (“HAIM”); reasonable
Gini coefficients.
Optimal monetary-fiscal policy (Ramsey) substantially altered relative to standard model.
I NTRODUCTION
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A DDITIONAL RECENT LITERATURE
Bullard and DiCecio (unpublished manuscript, St. Louis Fed, 2018):
Incomplete markets, nominal friction, heterogeneous households (“HAIM”); reasonable
Gini coefficients.
Optimal monetary policy repairs the distortion caused by the friction for all households.
See also the conference on “Monetary Policy and the Distribution of Income and
Wealth,” held at the St. Louis Fed on Sept. 11–12, 2015. Program available at https:
//research.stlouisfed.org/conferences/monetary_policy_conf/program.
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O UTLINE OF THE ARGUMENT
The role of monetary policy in this model is to make sure private credit markets are
working correctly (i.e., complete).
Optimal monetary policy in this model looks like “nominal GDP
targeting”—countercyclical price-level movements.
This result continues to hold even when there is “massive” heterogeneity—enough
heterogeneity to approximate income, financial wealth and consumption inequality
in the U.S.
Hence, the main result is that NGDP targeting constitutes “optimal monetary policy for the
masses” in this environment.
I NTRODUCTION
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Environment
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I NTRODUCTION
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L IFE - CYCLE MODELS
General-equilibrium life-cycle economy = many-period overlapping generations.
Key variables are privately issued debt, real interest rates and inflation.
Think of privately issued debt = “mortgage-backed securities.”
There is no government spending nor are there taxes of any kind.
C ONCLUSIONS
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S YMMETRY ASSUMPTIONS
We make a set of important “symmetry assumptions.”
These assumptions involve the symmetry of the life-cycle productivity endowment
pattern of the households (detailed below), along with log preferences, no
discounting and no population growth.
These assumptions help deliver the result that in the equilibria we study:
The real interest rate is exactly equal to the output growth rate at every date, even in the stochastic
economy.
We can think of this as the Wicksellian natural real rate of interest.
This in turn creates a set of easy-to-understand baseline results for this economy.
I NTRODUCTION
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E NVIRONMENT DETAILS
Standard (T + 1)-periods (quarterly) DSGE life-cycle endowment economy.
Each period, a new cohort of households enters the economy, makes economic
decisions over the next 241 periods, then exits the economy.
There is one asset in the model, privately issued debt (consumption loans).
The monetary authority controls the nominal price level P (t) directly.
For a money demand version, see Azariadis et al. (2015).
All households have log preferences with no discounting.
Other assumptions: No population growth, no capital, no default, flexible prices, no
borrowing constraints.
C ONCLUSIONS
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K EY FRICTION : NSCNC
Loans are dispersed and repaid in the unit of account—that is, in nominal terms—and are not
contingent on income realizations.
There are two aspects to this assumption.
The non-state contingent aspect means that real resources are misallocated via this friction.
The nominal aspect means that the monetary authority may be able to fix the distortion.
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L INEAR PRODUCTION TECHNOLOGY
We model a growing economy in which a linear technology is improving over time.
Aggregate real output Y (t) is given by
Y (t) = Q (t) L (t) ,
(1)
where L (t) is the aggregate labor input and Q (t) is the level of technology (also TFP
and labor productivity).
The level of technology grows at a stochastic rate λ (t, t + 1) between dates t and t + 1,
Q (t + 1) = λ (t, t + 1) Q (t) ,
where the stochastic process for λ is defined on the next slide.
(2)
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S TOCHASTIC STRUCTURE
The real wage w (t) is then exogenously given by
w (t + 1) = λ (t, t + 1) w (t) ,
(3)
where w (0) > 0, and λ (t, t + 1) is the gross rate of aggregate productivity growth
between date t and date t + 1. This growth rate is given by
λ (t, t + 1) = (1 − ρ) λ̄ + ρλ (t − 1, t) + σe (t + 1) ,
(4)
where λ̄ > 1 represents the average gross growth rate, ρ ∈ (0, 1) , σ > 0, and e (t + 1)
is a truncated normal with bounds ±b, b > 0, such that the ZLB is avoided.
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T IMING PROTOCOL
At the beginning of date t, nature moves first and chooses λ (t − 1, t) , which implies a
value for w(t).
The policymaker moves next and chooses a value for P (t) .
Households then decide how much to work, consume and save.
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N OMINAL INTEREST RATE CONTRACTS
Households meet in a large competitive credit market.
Households contract by fixing the nominal interest rate one period in advance.
The non-state contingent nominal interest rate, “the contract rate,” is given by
ct (t)
P (t)
−1
n
R (t, t + 1) = Et
.
ct (t + 1) P (t + 1)
This rate can be understood as expected nominal GDP growth.
In the equilibria we study, this expectation is the same for all households, even for
those born at different dates or with different levels of productivity.
(5)
I NTRODUCTION
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W HAT MONETARY
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POLICY DOES
The countercyclical price-level rule delivers complete markets allocations:
P (t) =
Rn (t − 1, t)
P (t − 1) ,
λr (t − 1, t)
(6)
where λr indicates a realization of the shock and Rn is the expectation given in the
previous slide—similar to Sheedy (BPEA, 2014) and Koenig (IJCB, 2013).
Given this policy rule, households consume equal amounts of available production
given their productivity, “equity share contracting,” which is optimal under homothetic
preferences.
This price-level rule renders the households’ date-t decision problem deterministic
because it perfectly insures the household against future shocks to income.
Consumption and asset holdings fluctuate from period to period but in proportion to
the value of w (t) .
I NTRODUCTION
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Life-Cycle Productivity
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L IFE - CYCLE PRODUCTIVITY PROFILES
Households entering the economy draw a scaling factor x ∼ U ξ −1 , ξ and receive a
life-cycle productivity profile that is a scaled version of the baseline profile, es :
es,i = x · es ,
where ξ ≥ 1 determines the within-cohort dispersion.
This process means all idiosyncratic risk is borne by agents at the beginning of the life
cycle.
Huggett, Ventura and Yaron (AER, 2011) argue that differences in initial conditions
are more important than differences in shocks.
We also consider a lognormal distribution for x, creating an economy with arbitrarily
rich and poor households.
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AVERAGE LIFE - CYCLE PRODUCTIVITY
The baseline profile, es , is given by:
"
es = f (s) = 2 + exp −
s − 120
60
4 #
.
Profiles begin at a low value, rise to a peak in the middle period of life, and then
decline to the low value.
Once assigned, profiles do not change.
Life-cycle productivity profiles are symmetric.
Agents can sell productivity units available in a particular period in the labor market
at the competitive wage per effective efficiency unit.
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B ASELINE LIFE - CYCLE PRODUCTIVITY
4
3
2
1
0
0
60
120
180
240
quarters
F IGURE : Baseline endowment profile. The profile is symmetric and peaks in the middle period of
the life cycle.
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T HE MASS
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OF LIFE - CYCLE PRODUCTIVITY
4
F IGURE : The mass of endowment profiles: es,i ∼ es · U ξ −1 , ξ , es = 2 + exp − s−60120
, ξ = 6.5.
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S TATIONARY EQUILIBRIA
We let t ∈ (−∞, +∞) .
We only consider stationary equilibria under perfectly credible policy rules governing
P (t) .
We let R (t) be the gross real rate of return in the credit market.
∞
Stationary equilibrium is a sequence {R (t) , P (t)}t+=−
∞ such that markets clear,
households solve their optimization problems, and the policymaker credibly adheres
to the stated policy rule.
The key condition is that aggregate asset holding A (t) = 0 ∀t.
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S TATIONARY EQUILIBRIA
T HEOREM
Assume symmetry as defined above. Assume the monetary authority credibly uses the price level
rule ∀t. Then the general equilibrium gross real interest rate, R (t − 1, t) , is equal to the gross rate
of aggregate productivity growth, and hence the real growth rate of the economy, λ (t − 1, t) , ∀t.
C OROLLARY
For any two households that share the same productivity profile, consumption is equalized at each
date t.
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Characterizing the Equilibrium
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I NTRODUCTION
H OURS
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WORKED OVER THE LIFE CYLE
1
0.5
0
0
60
120
180
240
quarters
F IGURE : Leisure decisions (green), labor supply (blue) and fraction of work time in U.S. data, 19%
(red). The labor/leisure choice depends on the current-to-lifetime average productivity ratio.
Productivity profiles of the form es,i = x · es imply labor/leisure choices depend on age only.
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L ABOR INCOME MASS
F IGURE : Labor income profiles es,i (1 − `) w; ξ = 6.5, η = 0.21, and w = 1.
C ONCLUSIONS
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C ONSUMPTION MASS
F IGURE : Consumption mass (red) and labor income mass (blue) along the complete markets
balanced growth path with w (t) = 1. Under optimal monetary policy, the private credit market
reallocates uneven labor income into perfectly equal consumption for each productivity profile. The
consumption Gini is 31.8%, similar to values calculated from U.S. data.
I NTRODUCTION
N ET
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ASSET HOLDING MASS
F IGURE : Net asset holding mass by cohort along the complete markets balanced growth path.
Borrowing, the negative values to the left, peaks at stage 60 of the life cycle (age ∼ 35), while
positive assets peak at stage of life 180 (age ∼ 65). The financial wealth Gini is 72.7%, similar to
values calculated in U.S. data.
C ONCLUSIONS
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T HREE NOTIONS
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OF INCOME
Three notions of income:
1
Labor income,
Y1 = es,i [1 − `t (t + s)] w (t + s) ,
2
Labor income plus non-negative capital income,
at,i (t + s − 1)
Y2 = es,i [1 − `t (t + s)] w (t + s) + max [λ (t + s, t + s − 1) − 1]
,0 ,
P (t + s − 1)
3
The non-negative component of total income,
at,i (t + s − 1)
Y3 = max es,i [1 − `t (t + s)] w (t + s) + [λ (t + s, t + s − 1) − 1]
,0 .
P (t + s − 1)
Gini coefficients of income distributions: GY1 = 56.2%, GY2 = 51.6%, GY3 = 59.6%.
C ONCLUSIONS
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L ABOR INCOME + NON - NEGATIVE CAPITAL INCOME
F IGURE : Profiles of
labor income and non-negative capital income
es,i (1 − `) w + max (λ − 1) Pa , 0 ; ξ = 6.5, η = 0.21, and w = 1.
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C ONCLUSIONS
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C ONCLUSIONS
N ON - NEGATIVE TOTAL INCOME
F IGURE : Profiles of non-negative total income max es,i (1 − `) w + (λ − 1) Pa , 0 ; ξ = 6.5, η = 0.21,
and w = 1.
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Inequality
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C ONCLUSIONS
I NTRODUCTION
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D ENSITIES
Endowment
0.1
0.05
0
E QUILIBRIUM
I NEQUALITY
P OLICY
Labor income
1
0.5
0
10
Consumption
0.5
0
0
5
Wealth
0.02
0.01
0
0
2
0
0
100
F IGURE : PDFs of endowment, labor income, consumption and wealth. Note: The wealth subplot
omits a mass point (121/241) at 0.
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C ONCLUSIONS
D ATA ON INEQUALITY IN THE U.S.
Consumption (Heathcote, Perri and Violante, RED, 2010): GC,U.S. = 32%.
Income (CBO, 2016): pre-taxes/transfers GY,U.S. = 51%; post-taxes/transfers
GY,U.S. = 43%.
Financial wealth (Davies, Sandström, Shorrocks and Wolff, EJ, 2011): GW,U.S. = 80%.
I NTRODUCTION
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I NEQUALITY IN THE MODEL
Large amount of heterogeneity that depends in part on life-cycle productivity
dispersion.
Financial wealth is defined as the non-negative part of net assets.
We also consider lognormal productivity, ln (x) ∼ N µ, σ2 :
Allows for arbitrarily rich and arbitrarily poor households.
All distributions (wealth, income and consumption) are mixtures of lognormals (and δ
functions).
Gini coefficients can be computed with “paper and pencil.”
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C ONCLUSIONS
G INI COEFFICIENTS
Wealth
W
Y1
Income
Y2
Y3
51%
Consumption
C
U.S. data
80%
32%
Uniform
72.7%
56.2%
51.6%
59.6%
31.8%
Lognormal
72.4%
55.7%
51.1%
59.0%
32%
TABLE : Gini coefficients in the U.S. data and in the model with uniform and lognormal productivity.
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P RODUCTIVITY DISPERSION AND G INI COEFFICIENTS
Wealth
Labor income
Consumption
1
0.5
0
2
4
6
8
10
F IGURE : As the dispersion of productivity profiles, ξ, increases, the Gini coefficients increase. The
ordering GW > GY > GC is preserved.
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Policy
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I NTERPRETING MONETARY
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POLICY
The price-level rule characterizes policy by countercyclical price-level movements.
But the policy can also be interpreted more conventionally in interest rate terms.
Contracts are made understanding policy ...
And policy is made understanding contracts ...
Interest rate policy is a fixed point of this process.
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P OLICY CHARACTERIZATION
The nominal rate is determined one period in advance as the expected rate of
nominal GDP growth.
Wicksellian natural real rate = aggregate productivity growth rate, λ.
The nominal rate is always ratified ex post by the policymaker.
This makes the real rate = aggregate productivity growth rate = Wicksellian natural
real rate of interest.
“Just like the simple NK model.”
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N OMINAL GDP
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TARGETING
How can we interpret these results as NGDP targeting?
No persistence in productivity growth, ρ = 0: The expected rate of NGDP growth never
changes, and the economy never deviates from the NGDP path. “Perfect NGDP
targeting.”
Persistence in productivity growth, ρ > 0: The expected rate of NGDP growth fluctuates
persistently with the shock, and it takes longer to return to the balanced growth NGDP
path.
Nominal and real rates fall in a recession.
I NTRODUCTION
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OF A SHOCK
1.06
1.02
1.04
1
1.02
0
5
10
0
quarters
5
10
quarters
1.4
1.06
1.2
1.04
1.02
1
0
5
quarters
10
0
5
10
quarters
F IGURE : Monetary policy responds to a decrease in aggregate productivity, λ, by increasing the
price level in the period of the shock. Subsequently, inflation converges to its BGP value, π ∗ , from
below. The nominal interest rate drops in the period after the shock.
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Conclusions
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S UMMARY
This paper attributes observed levels of U.S. inequality to life-cycle effects in
conjunction with heterogeneous life-cycle productivity profiles.
All households in this model, regardless of their assigned life-cycle productivity
profile, face a problem of smoothing life-cycle consumption in a world with a credit
market friction, “non-state contingent nominal contracting.”
The monetary authority can remove this impediment to life-cycle consumption
smoothing for all households: “optimal monetary policy for the masses.”
Does monetary policy affect inequality? Yes, it improves consumption allocations,
alters the asset holding distribution and alters the income distribution by altering
hours worked.
@FedFRASER